/*
Happy Number
============

Write an algorithm to determine if a number n is "happy".

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.

Return True if n is a happy number, and False if not.

Example: 
Input: 19
Output: true
Explanation: 
12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1
*/

class Solution
{
  bool recursion(int n, set<int> &s)
  {
    if (n == 0)
      return false;
    if (n == 1)
      return true;
    if (s.find(n) != s.end())
      return false;

    s.insert(n);
    int newNum = 0;
    while (n)
    {
      int digit = n % 10;
      n = n / 10;
      newNum += digit * digit;
    }

    return recursion(newNum, s);
  }

public:
  bool isHappy(int n)
  {
    set<int> s;
    return recursion(n, s);
  }
};
